When we used the on-prem version of Confluence there was a Custom HTML option and I could remove the "More actions" items with a change to the css. I cannot find anyway to change the css in the cloud version. I used the following previously and it worked - but I don't see where to add this now. We need to remove the options for anonymous access.
<style type="text/css">
#action-menu-primary { display: none !important; }
#view-attachments-link { display: none !important; }
#action-view-history-link { display: none !important; }
#view-page-info-link { display: none !important; }
#view-in-hierarchy-link { display: none !important; }
#action-view-source-link { display: none !important; }
#view-resolved-comments { display: none !important; }
#action-export-word-link { display: none !important; }
</style>